The three-parameter model comprising a steady-state gain, time constant, and time delay is well known in the controls industry and may form the basis of numerous tuning methods for PID controllers. The three-parameter model represents an information-efficient means of characterizing HVAC systems and also most chemical engineering processes to a reasonable degree of accuracy, even when the actual order is very high. Although the three-parameter model can be identified in heuristic ways through the application of specific test signals, an automated method of identification is desired due to the existence of multiple minima in parameter estimation cost functions formulated from input and output measurements.
Because the order of the true system is normally not known a priori, application of any type of recursive estimation scheme to the above class of systems would normally require parallel identification of multiple model candidates. An appropriate order would then need to be determined based on some cost function. In HVAC systems, computational resources on control devices are often limited due to the low-cost nature of the industry. Parallel identification of a potentially large number of models might therefore require computational storage and processing capabilities in excess of what is typically available.
One approach for identifying time delay models from input-output measurements is to estimate the parameters in several models in parallel, each model having a different time delay. However, this approach is computationally expensive and cumbersome to implement on-line, especially when the range of possible time delay values is not known very accurately beforehand. Techniques for estimating time delays in certain types of discrete-time models have been proposed but these techniques only estimate the time delay to the nearest integer multiple of the sampling period. Moreover, the problem of having multiple minima still exists when trying to estimate the time delay more accurately, i.e., when not an exact integer multiple of the sample period.
Although discrete models such as the ARMAX model are very popular and easy to implement, these models suffer from a number of deficiencies. For example, any translation from physically meaningful continuous-time system representations requires non-linear transformations, such as matrix exponentiations. The continuous-time parameters then have a non-linearly distributed relationship with the discrete parameters, making it difficult to relate changes in the estimated parameters to an original parameter of interest. In addition, fixed sampling intervals are normally required for ARMAX and other similar discrete models and the selection of a sampling rate is a critical design decision. It is known that the optimum sampling rate for control and for system identification are normally not the same. Hence, certain adaptive control methods based on discrete models suffer from sub-optimal sampling rates in either the control or identification aspect. In addition, anti-aliasing filters and other signal processing elements that are needed for robust estimation of the discrete model form end up becoming part of the estimated process model.
Accordingly, it would be advantageous to provide a system and method for characterizing a system. It would also be advantageous to adopt a “state variable filter” (SVF) method as a mechanism for directly estimating the parameters in a continuous-time model from input-output measurements. Direct estimation of continuous-time parameters offers several advantages over the discrete-time methods mentioned above. Most notably, the SVF method is less sensitive to sampling rates and is more amenable to the development of techniques for the estimation of a continuous-value time delay. The present invention demonstrates the latter advantage by developing a new transformation for obtaining the parameters in the desired first-order plus time delay characterization from parameters estimated in the continuous-time model. This approach yields near-optimal parameter estimates for given input-output data sets. The overall parameter estimation method is implemented as an automated testing tool that automatically applies step changes to the process under investigation, where the duration of each step is dynamically determined from the estimated parameters. Accordingly, it would be desirable to provide a system and method that allows systems, such as HVAC systems, to be automatically tested to validate performance, tune control loops, and configure controllers.
It would be desirable to provide for a system and method for an automated testing tool having one or more of these or other advantageous features.